Some Estimates of Schrödinger-Type Operators with Certain Nonnegative Potentials

We consider the Schrödinger-type operator H=(−Δ)2+V2, where the nonnegative potential V belongs to the reverse Hölder class Bq1 for q1≥n/2,  n≥5. The Lp estimates of the operator ∇4H−1 related to H are obtained when V∈Bq1 and 1<p≤q1/2. We also obtain the weak-type estimates of the operator ∇4H−1...

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Main Authors: Yu Liu, Youzheng Ding
Format: Article
Language:English
Published: Wiley 2008-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2008/214030
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author Yu Liu
Youzheng Ding
author_facet Yu Liu
Youzheng Ding
author_sort Yu Liu
collection DOAJ
description We consider the Schrödinger-type operator H=(−Δ)2+V2, where the nonnegative potential V belongs to the reverse Hölder class Bq1 for q1≥n/2,  n≥5. The Lp estimates of the operator ∇4H−1 related to H are obtained when V∈Bq1 and 1<p≤q1/2. We also obtain the weak-type estimates of the operator ∇4H−1 under the same condition of V.
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issn 0161-1712
1687-0425
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publishDate 2008-01-01
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-8fcaaa6403cf493285bc939f84dc74dd2025-08-20T02:09:29ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/214030214030Some Estimates of Schrödinger-Type Operators with Certain Nonnegative PotentialsYu Liu0Youzheng Ding1Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083, ChinaCollege of Science, Shandong Jianzhu University, Jinan 250101, Shandong Province, ChinaWe consider the Schrödinger-type operator H=(−Δ)2+V2, where the nonnegative potential V belongs to the reverse Hölder class Bq1 for q1≥n/2,  n≥5. The Lp estimates of the operator ∇4H−1 related to H are obtained when V∈Bq1 and 1<p≤q1/2. We also obtain the weak-type estimates of the operator ∇4H−1 under the same condition of V.http://dx.doi.org/10.1155/2008/214030
spellingShingle Yu Liu
Youzheng Ding
Some Estimates of Schrödinger-Type Operators with Certain Nonnegative Potentials
International Journal of Mathematics and Mathematical Sciences
title Some Estimates of Schrödinger-Type Operators with Certain Nonnegative Potentials
title_full Some Estimates of Schrödinger-Type Operators with Certain Nonnegative Potentials
title_fullStr Some Estimates of Schrödinger-Type Operators with Certain Nonnegative Potentials
title_full_unstemmed Some Estimates of Schrödinger-Type Operators with Certain Nonnegative Potentials
title_short Some Estimates of Schrödinger-Type Operators with Certain Nonnegative Potentials
title_sort some estimates of schrodinger type operators with certain nonnegative potentials
url http://dx.doi.org/10.1155/2008/214030
work_keys_str_mv AT yuliu someestimatesofschrodingertypeoperatorswithcertainnonnegativepotentials
AT youzhengding someestimatesofschrodingertypeoperatorswithcertainnonnegativepotentials